We report on highly efficient second, third and fourth harmonic generation from a femtosecond erbium-doped fiber source operating at 98 MHz repetition rate. By use of quasi-phase-matching in fan-out poled MgO:LiNbO3, we generate pulses at 770 nm, 520 nm and 390 nm, with corresponding average powers of 120 mW, 55 mW and 6 mW, respectively. Our device can be employed as a two-color source providing radiation from ultraviolet to near infrared.
© 2006 Optical Society of America
Based on recent advance in fiber laser technology, the potential for the development of a new range of nonlinear devices is emerging. These devices could cover a wide spectral range from ultraviolet to infrared and meet numerous applications, from time resolved spectroscopy, to biological imaging and photomedicine. Early work on frequency conversion of a femtosecond Er:doped fiber laser [1,2], resulted in second harmonic generation (SHG) with up to 8.7 mW of output power at 31.8 MHz repetition rate and a wavelength of 771 nm. In an additional setup, the SHG output was utilized to pump a parametric generator accessing the 1–3 μm range . More recently, we have demonstrated efficient frequency conversion of the near-infrared output from a femtosecond Er:doped fiber source into the visible . Continuously tunable sub-picosecond pulses in the range 520 nm to 700 nm were collected with average power levels up to 9.5 mW at a 97 MHz repetition rate. By use of Er:fiber lasers operating in the nanosecond time scale, highly efficient second and cascaded third harmonic generation (via sum frequency of two independent fiber sources) have also been reported . In this case a Ti:sapphire laser was employed as a master oscillator. Nanosecond pulses from an Er:fiber system were also used to synchronously pump an optical parametric oscillator, delivering a tunable output in the 2.55 μm - 3.96 μm range at a repetition rate of 500 Hz .
In this letter we present frequency doubling of a femtosecond Er:fiber source, with power levels increased by more than one order of magnitude compared to Refs 1 and 2. Similar conversion efficiencies have been observed from a cladding pumped Er-Yb fiber-amplifier operating at the somewhat longer wavelength of 1.62 μm . The high intensities at the second harmonic allowed us to generate more than 50 mW of third harmonic at green, by use of sum frequency mixing in a subsequent step, as well as 6 mW of fourth harmonic into the ultraviolet (UV). We believe that this is the first report of third and fourth harmonic generation from a fiber laser in the femtosecond regime.
2. Experimental set-up and pump source specifications
A schematic of our device is illustrated in Fig. 1. The two-branch pump source has been described in detail previously . In summary, it comprises a single erbium fiber oscillator mode-locked via nonlinear polarization rotation [9,10]. The oscillator is driven by a laser diode chip emitting 175 mW at 980 nm. It provides 2 mW of average power at a central wavelength of 1.55 mm and a repetition rate of 98 MHz. The output of the oscillator is split into two identical components which are used as seed radiation for the two parallel amplifier stages. A comprehensive study of the amplifier design can be found in . Each of the amplifiers is bi-directionally pumped by two 980 nm laser diodes with an overall cw-power of 1.3 W. The synchronous and mutually coherent output pulses from the two amplifiers are passed through silicon prism pairs for dispersion compensation.
An infrared spectrometer and a frequency resolved optical gating (FROG) apparatus based on second harmonic generation in a 50-μm thick barium-borate crystal were employed for spectral and temporal characterization of the pump pulses . Each branch of the pump source delivers sub-80 fs pulses centered at 1.55 μm with a spectral FWHM bandwidth of 60 nm. These values correspond to a time-bandwidth product ΔνΔτ < 0.6 indicating nearly transform limited pulses. Average power levels of 300 mW were obtained from each arm. In combination with a 98 MHz repetition rate, this value translates into pulse energies of 3 nJ. Enhanced performance of the present source compared to Ref. 11 is predominantly a result of higher power diode lasers.
For the generation of the cascaded harmonics three single-pass nonlinear converters were constructed. They comprise electrically poled, MgO doped LiNbO3 crystals with gradually varying grating periods Λ (fan-out design) [12,13]. This material system offers a large nonlinear coefficient and optical transparency in the wavelength range between 350 nm and 4500 nm allowing the propagation of up to the fourth harmonic of the fundamental wavelength. The orientation of the nonlinear crystals was chosen for the conventional e + e → e interaction with all waves polarized along the z - optic axis and use of the maximum nonlinear coefficient d33. The facets of the crystals were optically polished but not all of them were antireflection coated (see Table 1). The fan-out design ensures that the required period for a quasi-phase-matched (QPM) process is readily available by linear translation of the crystals, without stringent requirements in temperature control. All crystals were mounted on a copper plate, which was connected to a heating resistor; elevating the temperature to 60 °C ensured that photorefractive damage is avoided. The length of the crystals was 2 mm (1 mm) for the frequency doubling (tripling and quadrupling) stages, respectively. These values are approximately one order of magnitude larger than the corresponding group-velocity-mismatch (GVM) characteristic length. This fact leads to a focusing-dependent temporal broadening of the generated pulses , but offers higher conversion efficiencies. The QPM structures had a duty cycle of 0.5 and an order m = 1 (m = 3) for the frequency doubling and tripling (quadrupling) geometries, respectively. A QPM order of m = 1 for the quadrupling crystal would of course be preferable, but requires a sub-2.5 μm grating period. Fabricating a structure with such short periodicity constitutes a significant challenge for the current status of electric field poling technologies.
Two half-wave plates were used to control the polarization of the two fundamental beams. Each of the three frequency converting stages included an input focusing and an output collimating lens, chosen for nearly confocal geometries. The first amplifier is used to generate the second harmonic of the pump radiation. By use of a flipper mirror, the second harmonic beam can either a) pump in series the fourth harmonic converter, or b) be mixed with the fundamental from the second amplifier to generate the third harmonic. In the later case, spatial overlap between beams at ω and 2ω is achieved via a dichroic mirror (T > 90% at 1.5 μm – 2 μm and R > 99% at 1.1 μm – 1.4 μm), while temporal overlap is achieved by use of a computer-controlled translation stage. Table 1 summarizes the specifications of optical elements and nonlinear crystals employed in our set-up, and Table 2 lists the group velocity mismatch values between the different harmonics.
3. Device characterization
3.1 Second harmonic output
Figure 2 illustrates a selection of typical spectra obtained at the output of the frequency doubler. A maximum power of 120 mW was collected at a central wavelength of 770 nm. Accounting for an available fundamental average power of 300 mW we obtain an overall conversion efficiency (defined as P2ω/Pω) of 40 %. By linear translation of the crystal the second harmonic output was tunable in a 50 nm wide band between 750 nm and 800 nm. The FWHM bandwidth of the SHG signal varied from 2.5 nm to 6 nm. These values are in reasonable agreement with theoretical calculations in the plane wave approximation, which indicated a SHG acceptance bandwidth of 2.5 nm. Additional broadening of the SHG spectra should be attributed to off-axis and non-collinear conversion processes from neighbor gratings in the fan-out design. The narrow generated bandwidths imply that the SHG process utilizes only a small fraction of the broad fundamental spectrum. This comes as a contradiction to the large SHG conversion efficiencies. This effect has been observed and discussed in more detail previously , and can be understood via sum-frequency-mixing (SFM) contributions from input frequency components which are positioned symmetrically with respect to the fundamental central frequency. It is evident that, due to its spectral symmetry, the generalized SFM interaction is stronger at the center of the SHG tuning range and reduces in the wings. Not only is this depicted in the scaling of the generated power (which maximizes at the center of the SHG tuning range), but also in the profiles of the output spectra: the strong coexistence of SFM in the center of the SHG tuning range results in a smoothening of the output spectra. On the contrary, in the wings (where the pure SHG interaction dominates) the local structures of the input spectrum are conveyed in the output.
The dependence of the SHG average power on the fundamental average power, for an SHG wavelength of 770 nm, is shown in Fig. 3(a). The quadratic response is verified at low power levels, while significant gain saturation is observed above ~150 mW of input power. Frequency resolved optical gating was used for temporal characterization of the generated SHG pulses. Durations between ~140 fs and ~250 fs were measured within the tuning range of the SHG output without any external elements for dispersion compensation. Figure 3(b) shows a typical FROG trace indicating 142 fs chirp-free pulses at a wavelength of 775 nm with a spectral bandwidth of 3.9 nm. The measured pulse durations are significantly shorter than estimated theoretical values considering unfocused beams and group-velocity-mismatch. We attribute the pulse shortening in our experimental results to focusing effects .
3.2 Third harmonic output
The generated second harmonic output (120 mW) was mixed with the fundamental from the second amplifier (300 mW) for the generation of the third harmonic at 520 nm. Figure 4 shows a typical spectrum collected at the output of the frequency tripler stage. We obtained up to 55 mW of average power in the green. Taking into account that in this case both amplifiers are employed, and thus the total initial power at the fundamental wavelength is 600 mW, we obtain an overall conversion efficiency (defined as P3ω / Pω) of 9.2 %. The quantum conversion efficiency for the second harmonic pump beam (defined as N 3ω / N 2ω, where N indicates the number of photons at the corresponding frequency) exceeds 30 %. Due to the fact that the input facet of the nonlinear crystal, as well as the input focusing lens, were not coated, we estimate that less than 85 % of the available pump power was actually coupled into the nonlinear crystal. This finding indicates that average power levels as high as 75 mW can be generated at the third harmonic from our current set-up by minimizing losses.
Figure 5(a) illustrates experimental measurements of the third harmonic average power as a function of the fundamental and second harmonic pump powers. We observe a linear dependence on each of the two pump beam power levels, demonstrating the overall quadratic nature of the process and lack of gain saturation. A second-harmonic-autocorrelator based on a LiB3O5 crystal was used for determining the pulse duration at the third harmonic. A typical pulse profile is shown in Fig. 5(b). It reveals durations of 285 fs at 520 nm, assuming sech2 pulses. Combined with a spectral FWHM bandwidth of 2.18 nm, this value leads to a time-bandwidth product of ΔνΔτ~ 0.69. An additional prism compressor will be sufficient to remove the linear chirp and provide transform-limited pulses as short as ~150 fs. Contrary to the case of SHG, in this sum frequency process three distinct wavelengths are interacting. Therefore, to understand the temporal evolution of the process we need to account for GVM between the fundamental and a) the second harmonic (340 fs/mm), and b) the third harmonic (3 ps/mm). The first of these GVM values sets an upper limit to the interaction length (~0.5 mm accounting for typically 150 fs pump pulses at the second harmonic). The second value dominates the pulse duration of the generated field and explains the temporal broadening of the third harmonic pulses.
3.3 Fourth harmonic output
The second harmonic output was also frequency doubled in an additional stage to obtain the fourth harmonic wavelength in the ultraviolet. Figure 6 shows a typical output spectrum centered at 390 nm with a FWHM bandwidth of 1.5 nm and a corresponding average power of 6 mW. This amount of generated power, in combination with 120 mW of available input power, translates into an overall efficiency for the frequency quadrupler (defined as P 4ω/P 2ω) of 5 %. Since no coating was applied to the nonlinear crystal, or the input focusing lens, we estimate coupling and collection efficiencies that do not exceed 86 % and 83 %, respectively. Therefore, as much as 7.2 mW of UV light was generated inside the crystal for only 102 mW of pump power, indicating an overall internal efficiency of 7 %.
The predominant power-limiting factor in this process is the use of third order QPM. As discussed previously, a first-order QPM interaction would increase the conversion efficiency by a factor of 9 resulting in the generation of up to 50 mW of UV radiation. Although the fabrication of first order QPM gratings for this particular interaction involves a great amount of technical complexity, recent developments in short-period poling technologies [16,17] indicate that improvement of our current set-up is a realistic possibility. For the generation of the fourth harmonic, we have also employed a 1-mm long BiB3O6 crystal in a type I phase-matching geometry . The BiB3O6 option offers an additional tuning capability within the ~380 nm to 390 nm wavelength range, but limits the generated UV power to a maximum of 2.5 mW. No temporal measurements for the UV radiation were carried out. However, accounting for a GVM as large as 2.5 ps/mm, we estimate that the generated fourth harmonic pulses are well within the 1-picosecond range.
3.4 Summary of device performance
Our set-up delivers pulses at four consequent frequency harmonics at a repetition rate of 98 MHz. Table 3 summarizes the performance characteristics of our device. The three left columns indicate maximum power levels and corresponding pulse durations for each one of the individual outputs. This system, however, may be applicable to situations where two synchronised outputs at different wavelengths are required simultaneously (e.g, for pump-probe spectroscopy applications). The last two columns in Table 3 identify possibilities of operation in a two colour fashion; here, possible pairs of output wavelengths (λ1 / λ2), along with respective average power levels (P1 / P2), are marked.
We have demonstrated highly efficient second, third and fourth harmonic generation of a two-branch femtosecond Er:doped fiber source in MgO:LiNbO3. We obtained remarkable conversion efficiencies at the second harmonic wavelength of 770 nm, with corresponding average power levels of up to 120 mW. The strong SHG signal enabled us to efficiently generate the third and fourth harmonics of this laser in two additional stages, at wavelengths of 520 nm and 390 nm, and power levels of 55 mW and 6 mW, respectively. Temporal measurements revealed pulse durations as short as 140 fs (285 fs) at the second (third) harmonic, respectively. The applicability of our set-up as a two-colour source has been discussed. Finally, it has been shown that significant space for further improvement of our device characteristics exists.
The authors wish to thank TOPTICA Photonics AG for technical support and assistance.
References and links
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